The Lyapunov order for real matrices

Nir Cohen; Izchak Lewkowicz

doi:10.1016/j.laa.2008.10.020

The Lyapunov order for real matrices

Nir Cohen, Izchak Lewkowicz

Department of Electrical & Computer Engineering

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

The real Lyapunov order in the set of real n × n matrices is a relation defined as follows: A ≤ B if, for every real symmetric matrix S, SB + B^t S is positive semidefinite whenever SA + A^t S is positive semidefinite. We describe the main properties of the Lyapunov order in terms of linear systems theory, Nevenlinna-Pick interpolation and convexity.

Original language	English
Pages (from-to)	1849-1866
Number of pages	18
Journal	Linear Algebra and Its Applications
Volume	430
Issue number	7
DOIs	https://doi.org/10.1016/j.laa.2008.10.020
State	Published - 1 Apr 2009

Keywords

Controllability
Convex cone
Convex invertible cone
Lyapunov matrix equation
Pick matrix

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/j.laa.2008.10.020

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title = "The Lyapunov order for real matrices",

abstract = "The real Lyapunov order in the set of real n × n matrices is a relation defined as follows: A ≤ B if, for every real symmetric matrix S, SB + Bt S is positive semidefinite whenever SA + At S is positive semidefinite. We describe the main properties of the Lyapunov order in terms of linear systems theory, Nevenlinna-Pick interpolation and convexity.",

keywords = "Controllability, Convex cone, Convex invertible cone, Lyapunov matrix equation, Pick matrix",

author = "Nir Cohen and Izchak Lewkowicz",

note = "Funding Information: Corresponding author. E-mail addresses: nir@ime.unicamp.br (N. Cohen), izchak@ee.bgu.ac.il (I. Lewkowicz). 1 Supported by the Conselho Nacional de Pesquisa (CNPq), Brazil.",

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AU - Lewkowicz, Izchak

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N2 - The real Lyapunov order in the set of real n × n matrices is a relation defined as follows: A ≤ B if, for every real symmetric matrix S, SB + Bt S is positive semidefinite whenever SA + At S is positive semidefinite. We describe the main properties of the Lyapunov order in terms of linear systems theory, Nevenlinna-Pick interpolation and convexity.

AB - The real Lyapunov order in the set of real n × n matrices is a relation defined as follows: A ≤ B if, for every real symmetric matrix S, SB + Bt S is positive semidefinite whenever SA + At S is positive semidefinite. We describe the main properties of the Lyapunov order in terms of linear systems theory, Nevenlinna-Pick interpolation and convexity.

KW - Controllability

KW - Convex cone

KW - Convex invertible cone

KW - Lyapunov matrix equation

KW - Pick matrix

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JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 7

ER -

The Lyapunov order for real matrices

Abstract

Keywords

ASJC Scopus subject areas

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